A Mathematical Introduction to Geometric Quantization
Kadri \.Ilker Berktav, Burak O\u{g}uz, \"Omer \"Onder, Yunus Emre Sargut, Ba\c{s}ar Deniz Sevin\c{c}, Deniz Nazif Ta\c{s}tan
TL;DR
This paper provides a detailed mathematical overview of geometric quantization, covering symplectic geometry, formalism, and applications to knot theory, aimed at advancing understanding of the formalism's mathematical foundations.
Contribution
It offers a comprehensive exposition of geometric quantization formalism with new insights into its mathematical structure and applications to topology and knot theory.
Findings
Clarifies the mathematical structure of geometric quantization
Connects geometric quantization to knot theory and topology
Provides detailed background in symplectic geometry
Abstract
These notes are based on a series of lectures by Kadri \.Ilker Berktav from May 2024 to November 2024, providing a detailed exposition of geometric quantization formalism and its essential components. They are organized into three parts: background in symplectic geometry, basics of geometric quantization formalism, and an application related to Edward Witten's work in knot theory and topology.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Advanced Algebra and Geometry